Mathematical modeling tools are an integral part of any groundwater management system. These are required to predict spatio-temporal variations of groundwater level in an aquifer system in response to recharge and pumping. These modeling tools fall under two categories: (i) analytical and (ii) numerical. While numerical methods are able to incorporate aquifer heterogeneities in the groundwater management system, analytical methods give exact solutions of groundwater flow problems having simple aquifer systems and are fast in terms of computation time.
In an article, Baumann (1952) derived analytical solution to describe growth of the groundwater mound in sloping aquifers receiving vertical recharge. In another article, Glover (1960) developed analytical solution for the growth of water table in an infinite unconfined aquifer induced by recharge from a circular area. In another work, Hantush (1967) developed solutions for the growth and decay of water table in infinite unconfined aquifers in response to recharge from circular and rectangular recharge basins. In yet another article, Warner et al. (1989) reviewed the performance of analytical solutions developed by Baumann (1952), Glover (1960), Hantush (1967), Hunt (1971), and Rao and Sarma (1981). These analytical solutions are based on the assumption of constant rate of recharge and were developed for a single recharge basin. Zomorodi (1991) used observed water table fluctuation data to show that the analytical solution of Dagan (1966) based on the assumption of constant rate of recharge lead to erroneous results in the case of time varying recharge rate.
In one article, Dagan (1964) derived analytical solution to describe water table fluctuations in a drainage system receiving step-wise time varying recharge. In another article, Singh and Jacob (1977) developed analytical solutions for groundwater flow in an unconfined aquifer for constant and variable rates of recharge and withdrawal. They approximated variable rates of recharge and withdrawal by periodic step functions. In another article, Rai et al. (1994) developed analytical solution for exponential recharge rate from a single basin. These analytical solutions were developed for a single recharge basin.
In an article, Manglik and Rai (2000) developed analytical solution to model water table fluctuations in an isotropic unconfined aquifer in response to time varying recharge from multiple rectangular basins. This solution incorporates prescribed head boundary conditions and approximates wells as rectangular discharge basins of very small dimension. In yet another article, Manglik et al. (2004) developed analytical solution to describe water table variation in the presence of time varying recharge and pumping from any given number of recharge basins with the prescribed zero flux boundary conditions. These solutions were developed under the assumption of isotropic aquifer. Present invention describes a more generalized analytical solution for an anisotropic unconfined aquifer.
The main object of the present invention is to provide a method of predicting the dynamic behavior of water table in an anisotropic unconfined aquifer having a general time-varying recharge rate from multiple rectangular recharge basins.
Another object of the present invention is to provide analytical method for validation of numerical schemes which are used to model real field problems of groundwater flow.
Yet another object of the present invention is to provide analytical method for sensitivity analysis of various controlling parameters such as physical properties of aquifer, nature of recharge rate, and distribution of recharge basins within the aquifer.
A further object of the invention is to provide a digital implementation of the analytical method for modeling of the groundwater flow in an anisotropic unconfined aquifer for a general time-varying rate of recharge from multiple rectangular recharge basins.
The present invention provides a method of predicting the dynamic behavior of water table in an anisotropic unconfined aquifer having a general time-varying recharge rate from multiple rectangular recharge basins, the said method comprising the steps of setting up of a second order diffusion equation describing groundwater flow in an anisotropic unconfined aquifer having finite length and width along X and Y directions, respectively, prescribing different combinations of Dirichlet (prescribed head) and Neumann (zero flux) conditions at the boundaries of the aquifer, prescribing the locations and dimensions of various rectangular recharge basins located within the aquifer, prescribing a general time-varying recharge function as the source term in the diffusion equation to describe rates of recharge for each of the recharge basins, solving the above said system of equations by using finite Fourier transform method to obtain analytical solution for the prediction of spatial and temporal variation of water table and finally, digitally implementing the analytical solution for prediction of dynamic behavior of water table in response to applied time varying recharge